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**1. Homework Statement**

Prove that ([tex]\sum_{j=1}^n[/tex]a

_{j}b

_{j})

^{2}<= ([tex]\sum_{j=1}^n[/tex]ja

_{j}

^{2})([tex]\sum_{j=1}^n[/tex](1/j)b

_{j}

^{2})

**2. Homework Equations**

Cauchy-Schwarz Inequality: |<u, v>| <= ||u||*||v||

**3. The Attempt at a Solution**

If I let u = [tex]\sum_{j=1}^n[/tex]ja

_{j}

^{2}and v = [tex]\sum_{j=1}^n[/tex](1/j)b

_{j}

^{2}, then I have ||u|| = sqrt(<u, u>) and ||v|| = sqrt(<v, v>). Not really sure where to go from here. Any ideas? Thanks!